A motor outputs power of 500 watts and is used to raise a 5kg mass vertically at
constant speed. How long in seconds does it take to raise the mass 15 meters?
PE=mgh
5*9.8*15= 735
Power= Energy/time so..
t=E/P
t=735/500
t=1.47
To solve this problem, we need to use the formula for mechanical power:
Power = Force x Velocity
In this case, the force is equal to the weight of the mass being raised, which is given by:
Force = mass x gravity
Where:
mass = 5 kg (given)
gravity = 9.8 m/s^2 (acceleration due to gravity)
Therefore, the force is:
Force = 5 kg x 9.8 m/s^2 = 49 N
Given that the power output of the motor is 500 watts, we can rearrange the formula for power to solve for velocity:
Velocity = Power / Force
Substituting the values, we have:
Velocity = 500 watts / 49 N ≈ 10.2 m/s
Now we can use the formula for average velocity to find the time it takes to raise the mass:
Velocity = Distance / Time
Let Time be the unknown.
Rearranging the formula, we have:
Time = Distance / Velocity
Substituting the values, we have:
Time = 15 meters / 10.2 m/s ≈ 1.47 seconds
Therefore, it takes approximately 1.47 seconds to raise the 5kg mass 15 meters at a constant speed using the 500-watt motor.
To solve this problem, we need to use the concept of work and the formula for calculating work done.
First, we need to calculate the work done to lift the mass. The work done (W) is equal to the force (F) multiplied by the distance (d) moved in the direction of the force.
The force required to lift the mass is equal to the weight of the mass (mg), where m is the mass and g is the acceleration due to gravity (9.8 m/s²).
The distance moved is given as 15 meters.
So, the work done can be calculated as:
W = F * d = (mg) * d
Now, we need to find the time taken to do this work. The power (P) is defined as the work done per unit time. Mathematically, P = W/t.
Knowing the power output of the motor is 500 watts, we can rewrite the equation as:
P = W/t
500 = W/t
We have the expression for W from the earlier calculation. So we can substitute it into the equation:
500 = (mg) * d / t
We want to find the time taken to raise the mass, so we need to rearrange the equation to solve for t:
t = (mg) * d / 500
Plugging in the values we have:
m = 5 kg
g = 9.8 m/s²
d = 15 m
t = (5 * 9.8 * 15) / 500 = 0.294 seconds
Therefore, it takes approximately 0.294 seconds to raise the 5 kg mass vertically at a constant speed of 15 meters using the given motor.